g.region -ap raster=pop_dens
# Window size of 12 means 12 pixels of 30 arcsec = 6 mins = 0.1 degrees
r.neighbors input=pop_dens output=pop_dens_smoothed method=average size=12
# Recode the continuous raster to only three values at the breaks you need
r.recode input=pop_dens_smoothed output=pop_dens_recode rules=- <<EOF
0:500:0
501:1000:500
1000:99999:1000
EOF

r.to.vect input=pop_dens_recode output=pop_dens type=area column=density